People working in science are well aware that severe criteria are generally used to scrutinize their work, work that must appear on reputable journals where a review by peers decides the goodness or the rejection. This is generally the start of a procedure that can last several years and that should end up with the output of some experiments, at least for experimental science like physics. So, when some people, with none or very few publications get instantaneous fame by media hype the matter is suspicious since the start and some caution is in order. As an example, I would like to remember what happened to my work when someone took the braveness to put it in Wikipedia and the discussion that followed (see here). The final result was its removal after Peter Woit and all his gang claimed my head. This work just stand up through passing time and Terry Tao agreed on the correctness of the main theorem supporting all this and that was the foundation of the entry into the Yang-Mills article in Wikipedia (see here) after I provided a correct proof (see here). Currently, I keep on working on this and I keep on giving talks in international conferences about.
Lisi’s case is completely different and belongs to those with immediate hype with no substance at all. No serious file of publications just someone that, for some reason very difficult to understand, after a preprint appeared on arXiv became an immediate star. After all that fuss, serious people in the scientific community found serious drawbacks in that preprint that never saw the light in a reputable journal. Rather, Distler and Garibaldi showed that it was simply flawed in its claims as its author (see here). This paper appeared in a very prestigious mathematical physics journal.
In the world of mathematicians, after such a proof of wrongness, one should go off with his tail between his legs. This happened in the case of Deolalikar and the Np vs P Millenium problem and this is the way a sane community just works. But this did not happen in physics as we are coping with this matter even after it was proven wrong and was never seen on any refereed journal. There is an ongoing discussion at Wikipedia and an edit war at the Lisi’s article (see here and here). An interesting criticism is that Lisi’s page is wider than Nobel winners while he does not appear to have similar merits. By my side, I would just add that there are a lot of very good people with tons of publications and citations that would be worth a Wikipedia article and Lisi obtained a large one just thanks to a lot of media fuss. There is very few to say because this is Wikipedia but this is also not the right way to convey scientific information.
In the end, we are just tired of nothingness in science getting all this room. The right information should be conveyed and wrong theories should be simply forgotten everywhere independently on the fact that somebody used someone else.
Marco Frasca (2009). Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical
Case Mod. Phys. Lett. A 24, 2425-2432 (2009) arXiv: 0903.2357v4
Jacques Distler, & Skip Garibaldi (2009). There is no “Theory of Everything” inside E8 Commun.Math.Phys.298:419-436,2010 arXiv: 0905.2658v3
I am an avid reader of Wikipedia as there is always a lot to be learned. Surfing around I have found the article Yang-Mills existence and mass gap and the corresponding discussion page. Well, someone put out my name but this is not the real matter. A Russian mathematician, Alexander Dynin, presently at Ohio State University, was doing self-promotion on Wikipedia at his paper claiming to have found a solution to the problem. This is not published material, so Wiki Admins promptly removed it and started a discussion. By my side, I tried to make aware the right person for this and presently no answer come out. I cannot say if the proof is correct so far but, coming from a colleague, it would be a real pity not to take a look. Waiting for more significant judgments, I will take some time to read it.
Recently, I have posted on the site of Terry Tao and Jim Colliander, Dispersive Wiki. I am a regular contributor to this beautiful effort to collect all available knowledge about differential equations and dispersive phenomena. Of course, I can give contributions as a solver of differential equations in the vein of a pure physicist. But mathematicians are able to give rigorous theorems on the behavior of the solutions without really solving them. I invite you to take some time to look at this site and, if you are an expert, to register and contribute to it.
My recent contribution is about exact solutions of nonlinear equations. This is a really interesting field and most of the relevant results come from soliton theory. Terry posted on his blog about Liouville equation (see here). This equation is exactly solvable and is widely known to people working in string theory. But also one of the most known equations in physics literature can be solved exactly. My preprint shows this. Indeed I have to update it as, working on KAM theorem, I have obtained the exact solution to the following equation (check here on Dispersive Wiki):
that can be written as
being now the dispersion relation
As always is an arbitrary parameter with the dimension of a mass. You can see here an example of mass renormalization due to interaction. Indeed, from the dispersion relation we can recognize the following renormalized mass
that depends on the coupling. This class of solutions clearly show how the nonlinearities produce contributions to mass. Either by modifying it or by generating it. So, it is not difficult to imagine that Nature may have adopted them to display mass wherever there is not.
As a by-product, I am now able to give a consistent quantum field theory in the infrared for the scalar field (always thank to my work on KAM theorem), obtaining the needed corrections to the propagator and the spectrum. I hope to find some time in the next days to add all this new material to my preprint. Meanwhile, enjoy Dispersive Wiki!
I am a great estimator of Terry Tao and a reader of his blog. Tao is a Fields medalist and one of the greatest living mathematicians. Relying on such a giant authority may give someone the feeling of being a kind of dwarf trying to be listened around. Anyhow I will try. Terry come out with an intervention in Wikipedia here claiming:
“It may be relevant to point out that one of the references cited in the disputed section  has a significant error in it, despite being published. Namely, in the proof of Theorem 1, the author is assuming that an extremum A for the Yang-Mills action for a special class of connections (namely those in which and all other components vanish) is necessarily an extremum for the Yang-Mills action for all other connections also, but this is not the case (just because , for instance, for A’ of this special form, does not imply that for general A’). Since one needs to be an extremiser (or critical point) in the space of all connections in order to be a solution to the Yang-Mills equations, the mapping provided in Theorem 1 has not been shown to actually produce solutions to the Yang-Mills equation (and I suspect that if one actually checks the Yang-Mills equation for this mapping, that one will not in fact get such a solution). Terry (talk) 20:32, 28 February 2009 (UTC)”
This claim of mistake by my side contains a misinterpretation of the mapping theorem. If the theorem would claim that this is true for all connections, as Terry says, it would be istantaneously false. I cannot map a scalar field on all the Y-M connections (think of chaotic solutions). The theorem simply states that there exists a class of solutions of the quartic scalar field that are also solution for the Yang-Mills equations and this can be easily proved by substitution (check Smilga’s book) and Tao is proved istantaneously wrong. So now, what is the point? I have a class of Yang-Mills solutions that Tao is claiming are not. But whoever can check by herself that I am right. So, is Terry wrong?
Till now, I have avoided to feed this flooding about abuses on Wikipedia. But I think that a few words are needed in order to clarify my position and to let my own point of view widely known.
The problem started when Peter Woit took a look at the Yang-Mills entry of Wikipedia. He has found a section apparently self-promoting my work. What was about this section? The title said “Integrable solutions of classical Yang-Mills equations and QFT “. I think that there is a lot to say about this matter as classical solutions of Y-M exist and is well acquired matter. But in this section a class of solutions were put, cited in the Smilga’s book, that I have generalized and introduced in my papers. Should they be there? I think yes as they belong to the class of solutions stated in the title. They appear to be too recent for inclusion but this is plain mathematics. Mathematics is a two-way switch: It is either right or wrong and so, if these solutions are right, they should be there as a bookkeeping for the readers.
The worst question is anyhow self-promotion. On this ground Peter Woit did worst: He is self-promoting his book (see here , thank you Lubos). Promoting a book means to earn money for the author while promoting a scientific idea may have the right side that, being the idea good, a good service has been done to the community.
The worst aspect of the story has been the intervention of Woit through his blog. This is a perfect war machine that when activated may leave a lot of casualties. People should be smart at their defense as otherwise the risk is to be counted in that number. A flood of people moved toward Wikipedia with any means trying to remove the questioned section and attacking me and whoever has written it. A lot of comments in Woit’s blog was posted attacking me. I was forced to introduce moderation for comments in my blog. Of course this appears like a kind of lynching without any understanding of scientific merit. Curators of Wikipedia decided that majority was right and Woit have had his win: The section was finally removed.
What next? This situation is quite interesting by my side. The reason is that the physical matter is Yang-Mills theory that is one of the biggest open problems both in phyics and mathematics. There is a lot of very good people working on that in this moment and my view is that a complete understanding is at hand. Ask yourself this question: What would be Woit’s position if I am right? This is not like string theory that we do not know when a confirmation will be at hand. Here we have computers, accelerators and a lot of smart people crunching this problem. In a very short time an eventual Woit’s error will be exposed. And by irony, Wikipedia’s entry will be updated with my ideas. Much better than now.
The question to be asked is: Should Wikipedia support new material? Since the editors of scientific entries in Wikipedia are scientists themselves one cannot ask them impartiality. Science is a dynamic endeavor and Wikipedia a dynamic source of information. They should be merged to meet each other in the right way.
I would like to point out to my readers Scholarpedia. This represents a significant effort of the scientific community to grant a wiki-like resource with the benefit of peer-review. This means that articles are written on invitation and reviewed by referees chosen by the Editorial Board. This resource is important as correctness of information is granted by the review process and by the choice of the authors that are generally main contributors to the considered fields. It is interesting to point out that, currently, there are articles written by 15 Nobelists and 4 Fields medalists. The most relevant aspect to be emphasized is that the information is freely accessible to everybody exactly in the spirit of Wikipedia.
Wikipedia is doing a relevant service to our community. I have contributed to some voices both for the english and the italian version and I have used it a lot of time to make myself acquainted with some unknown parts of physics. I think that this is worthwhile a support:
As you will know since now I am a strong supporter of any kind of revolution and this is a big one.
So, long life to Wikipedia!